Question

An oil company is considering adding a more environmentally friendly grade of fuel 56 at its service stations. To do this, an additional 3600-gallon tank must be buried at each station. Discussions with tank fabricators indicate that the least expensive tank would be cylindrical with minimum surface area. What size tank should be ordered?

Answer 1

To determine the size of the tank, calculate the volume using the formula V = πr^2h. Minimize the surface area by considering the tank as a cylinder with minimum surface area ratio. Use the given information on gasoline to estimate the CO₂ emissions and adjust the tank size accordingly.

Step-by-step explanation:

To determine the size of the tank that should be ordered, we need to calculate the volume of the tank. In this case, the tank is cylindrical, so the volume can be calculated using the formula V = πr^2h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the tank, and h is the height or depth of the tank.

Since the goal is to minimize the surface area, we can consider the tank to be a cylinder with a minimum surface area. This can be achieved by minimizing the ratio of the height to the radius, which means the tank should be as close to a perfect cylinder as possible.

Using the given information, we know that one tank holds about 13 gallons of gasoline, and the density of gasoline is 0.75 kg/L. Therefore, the mass of one tank of gasoline is approximately 38 kg. Applying the ratio of CO₂ mass to input fuel mass, we find that one tank of gasoline will produce about 110 kg of CO₂.

Since the goal is to be more environmentally friendly, we can assume that the new grade of fuel produces less CO₂ than gasoline. Therefore, we can determine the size of the tank by considering the desired reduction in CO₂ emissions. For example, if the goal is to reduce CO₂ emissions by 50%, the new tank should be about half the size of the current tank.